Pricing swing options in electricity markets with two stochastic factors using a partial differential equation approach

Abstract

In this paper, we consider the numerical valuation of swing options in electricity markets based on a two-factor model. These kinds of contracts are modeled as pathdependent options with multiple exercise rights. From a mathematical point of view, the valuation of these products is posed as a sequence of free boundary problems, where two exercise rights are separated by a time period. In order to solve the pricing problem, we propose appropriate numerical methods based on a Crank-Nicolson semi-Lagrangian method combined with biquadratic Lagrange finite elements for the discretization of the partial differential equation. In addition, we use an augmented Lagrangian active set method to cope with the early exercise feature when it appears. Moreover, we derive appropriate artificial boundary conditions to treat the unbounded domain numerically. Finally, we present some numerical results to illustrate the proper behavior of the numerical schemes.

The Jump Size Distribution of the Commodity Spot Price and Its Effect on Futures and Option Prices

“…As we use nonparametric methods a closed-form solution cannot be found. Recently, several numerical methods have been developed to solve this kind of problems; see [38,39].…”

Valuation of Insurance Products with Shout Options in a Jump-Diffusion Model

“…In addition, some research results have demonstrated that the character of jumps has a tremendous influence on the value of options. Among these, the jump-diffusion model described more accurately than a Brownian motion [14][15][16][17][18][19][20]. Moreover, some models for describing the underlying asset were the stochastic volatility jump model [21,22], the double stochastic volatility model with jumps [23,24], etc.…”

Forest of Stochastic Trees: A Method for Valuing Multiple Exercise Options

“…In this paper, we replace the binomial and trinomial trees of Lari et al (2001) and Jaillet et al (2004) with the stochastic trees of Broadie and Glasserman (1997), hence creating the Forest of Stochastic Trees (FOST) method for valuing multiple exercise options. The FOST can be thought of as generalizations of two different methodologies; specifically, it extends valuation and control of energy production and storage facilities Chen and Forsyth (2007); Ludkovski and Carmona (2010); Thompson et al (2009); and (iv) swing options Calvo-Garrido et al (2017); Jaillet et al (2004); Lari et al (2001); Wilhelm and Winter (2008).…”

“…Discrete-time tree-based methods for valuing American-style options Cox et al (1979) have been extended to MEOs via the Forest of Trees Jaillet et al (2004); Lari et al (2001). Techniques for pricing American-style options using solutions of PDEs have been modified to MEOs Calvo-Garrido et al (2017); Chen and Forsyth (2007); Thompson et al (2009); Wilhelm and Winter (2008). These methods for MEOs inherit properties similar to the corresponding methods for single-exercise options.…”